03-09
On the existence of Hermitian-harmonic maps from complete Hermitian to complete Riemannian manifolds
by Grunau, Hans-Christoph; Kuehnel, Marco
Preprint series: 03-09, Preprints
The paper is published: Math. Z. 249 , 297-327 (2005).
- MSC:
- 53C42 Immersions (minimal, prescribed curvature, tight, etc.), See also {49Q05, 49Q10, 53A10, 57R40, 57R42}
- 35J60 Nonlinear PDE of elliptic type
- 35K55 Nonlinear PDE of parabolic type
Abstract: On non-K hler manifolds the notion of harmonic maps is modified to that of Hermitian harmonic maps in order to be compatible with the complex structure. The resulting semilinear elliptic system is not in divergence form. The case of noncompact complete preimage and target manifolds is considered. We give conditions for existence and uniqueness of Hermitian-harmonic maps and solutions of the corresponding parabolic system, which observe the non-divergence form of the underlying equations. Numerous examples illustrate the theoretical results and the fundamental difference to harmonic maps.
Keywords: Hermitian-harmonic maps, non-Kaehler manifolds, non-divergence form
Notes: Die aktuelle Klassifikation (MSC 2000) ist 53C44. Leider ist noch die alte Klassifikation (MSC1991) abgespeichert.
The author(s) agree, that this abstract may be stored asfull text and distributed as such by abstracting services.